When heated to a particular temperature range, certain alloys arc capable of undergoing enorinous plastic elongation, or strain, with uniform thinning throughout the full area of a metal sheet or blank. This characteristic, known as superplasticity. is used to form objects from such alloys by placing a metal sheet in a forming die containing a die cavity, heating the sheet to the desired temperature, and then applying a pressure differential to the respective sides of the sheet for a period of time. The pressure differential, known as the forming pressure, is obtained by introducing a pressurized inert gas into the sealed die on one side of the sheet, while the die cavity on the other side of the sheet contains an inert gas at a lower pressure, for example, atmospheric pressure. The forming pressure forms the heated metal sheet to the shape of the die cavity or the shape of a male die located in the die cavity.
Forming pressure and strain rate are related variables. Their relationship is affected by the superplasticity of the metal sheet, and by the geometry of the object to be formed. Using the critical assumption that the strain rate remains constant, a forming schedule, also called a pressure forming cycle, can be mathematically derived to provide the forming pressure as a function of forming time. The strain rate is empirically determined to be a value that is low enough to avoid rupturing the sheet during forming, yet high enough to form the desired object within a reasonable period.
An example of the foregoing approach is provided by Hamilton et al. in U.S. Pat. No. 4,233,829. As can be seen therein, the calculations necessary to derive the forming pressure versus time graph are complex and very time consuming, even for the simple geometry of a rectangular pan.
Hamilton et al. further disclose apparatus for automatically supplying the forming pressure called for by the pressure versus time graph to the forming die cavity. Others have used similar methods of mathematical analysis to produce graphs of forming pressure versus time, and then used other means to adjust the forming pressure in accordance with their respective graphs.
The problem inherent to the foregoing approaches is that any mathematical model used to obtain a graph of forming pressure versus time is only an approximation because the assumed value for the strain rate used in the model cannot be determined with any degree of certainty and, furthermore, the strain rate is assumed to remain constant whereas, in fact, it varies throughout the forming cycle as well as spatially across the forming sheet.
The relationship between the forming stress, .sigma., and strain rate, .epsilon., is expressed by the following equation: EQU .sigma.=K.epsilon..sup.m
wherein:
K is a forming constant; and PA1 m is the strain rate sensitivity.
A critical inaccuracy in the foregoing assumptions arises from the inherent nature of the strain rate sensitivity, m, which has an exponential effect in the relationship between stress, .sigma., and strain rate, .epsilon.. The strain rate sensitivity, m, is empirically known for most metallic alloys, or can be obtained from a forming test. However, m varies with the temperature and microstructure of the sheet, as well as with the forming stress, .sigma., and thus changes throughout the forming process. The empirical value for m is thus an approximation for the entire forming process, and the reliability of the pressure versus time graph will suffer as m varies due to the aforementioned factors.
The foregoing mathematical approaches also assume that the strain rate is the same over the entire surface of the sheet, whereas it actually varies from point to point over the sheet due to the sheet's changing geometry during forming, variations in the sheet's thickness, and temperature gradients. Their accuracy is also adversely affected by slippage of the sheet after it comes into contact with the interior surface of the die cavity. In addition, mathematical models fail to account for differences in superplasticity that inevitably occur among different sheets of the same alloy, caused by innate variations in the production process.
In summary, the assumptions and approximations necessary to the mathematical analysis for deriving the forming pressure as a function of time, introduce errors which adversely affect the reliability of the relationship, especially as the geometry of the object becomes more complex. This inaccuracy causes a difference between the actual position of the forming sheet and its predicted position. The forming pressure versus time graph does not correct for such deviations, with the result that an inappropriate forming pressure may be applied. Rupture may be the result.
Efforts have been made to monitor the deformation of the sheet so that the forming pressure can be adjusted to take into account a deviation of the actual position of the forming sheet from the predicted position and avoid rupture due to this problem. For example, in U.S. Pat. No. 4,489,579, Daime et al. show a hollow tube slideably projecting into the die cavity and having one end in contact with the sheet in order to measure the distortion of the sheet. Electrical monitoring devices are situated at each recess angle of the die cavity to inform of the arrival of the sheet. Further, Japanese Patent No. 1-210130 issued to Hisada shows a touch sensor slideably projecting into the die cavity. The sensor comes into contact at only one point on the sheet, and thus would not, be able to indicate how the sheet is forming in corners or other recesses in the die cavity.
Both of the foregoing approaches require breaching the die cavity, and thus add mechanical complexity and expense to the forming die. Furthermore, both require having a sensor in contact with the forming sheet. This will result in the area of the sheet in contact with the sensor being prevented from forming normally, thus affecting the strain rate and causing a discontinuity in material thickness in the formed object between the area that was in contact with the sensor and the adjacent area.
In U.S. Pat. No. 5,007,265, Mahoney et al. use a video camera to view reference marks on the sheet and thereby monitor its strain. The device described therein thus requires a special forming die having a window to allow observation of the forming sheet. Such a special forming die would clearly be more expensive to fabricate than a conventional forming die. A further drawback is that the sheet must be continually observed by the operator during the forming process, and therefore the use of the described apparatus does not lend itself to automation and the attendant savings in production cost.
Another approach to controlling superplastic forming is shown by Yasui in U.S. Pat. No. 5,129,248. The apparatus and method shown therein control the strain rate by measuring and regulating the flow rate of gas mass flowing into the forming die and displacing the sheet being formed. This is an advance over controlling forming by regulating pressure according to a predetermined relationship between pressure and time because it does not rely on the assumption that an empirically determined strain rate remains constant during the forming process and over the entire forming sheet. The possibility of rupture inherent in the use of a pressure versus time graph is thus avoided.
In U.S. Pat. No. 4,708,008, Yasui et al. show an apparatus for controlling the superplastic forming of a sheet by continuously monitoring the height of liquid in a manometer fluidly communicating with the gas being displaced and exhausted from a forming die cavity during forming, in conjunction with regulating the forming pressure responsive to the height of the liquid on the manometer. Beforming is begun, the use of the foregoing device requires an empirical or mathematical analysis to determine the relationship between the forming pressure and the location of the sheet as it is forming. The relationship between the forming progress of the sheet and the displaced volume of the exhaust gas is then determined.
The displaced volume is then converted into exhaust pressure, and the exhaust pressure is converted into the height of liquid in a manometer fluidly communicating with the exhaust gas. The foregoing relationships are used to drive the relationship between forming pressure and the height of liquid in the manometer, which is the relationship used to guide the forming process. Although this apparatus is useful for testing the forming of cylindrical shapes, the foregoing analyses can be complex.
Based on the foregoing, it can be appreciated that there presently exists a need for a method and apparatus to control superplastic forming which overcomes the above described disadvantages and shortcomings of the prior art. The present invention provides an apparatus in conjunction with a reliable yet simple method for regulating superplastic forming, and in so doing fulfills this need in the art.